曲线 r=a(1-cosφ) 为心形线,φ∈[0,2π]∫∫√(x^2+y^2)dxdy=∫dφ∫r*rdr=(1/3)∫[r^3]dφ=(a^3/3)∫(1-cosφ)^3dφ=(a^3/3)∫[1-3cosφ+3(cosφ)^2-(cosφ)^3]dφ=(a^3/3){2π+(3/2)∫(1+cos2φ)dφ-∫[1-(sinφ)...